1. 3-8 Equivalent Fractions and Mixed Numbers Warm Up
Course 2
3-8
Equivalent Fractions and Mixed Numbers
Warm Up
Name a common factor for each pair.
1. 5 and 10
2. 9 and 12
3. 20 and 24
4. 10 and 14
5. 6 and 8
6. 8 and 15
Possible answers: 5 3 4 2 2 1

2. Course 2
3-8
Equivalent Fractions and Mixed Numbers
Learn to identify, write, and convert between equivalent fractions and mixed numbers.

3. Insert Lesson Title Here
Course 2
3-8
Equivalent Fractions and Mixed Numbers
Insert Lesson Title Here
Vocabulary
equivalent fractions
improper fractions
mixed number

4. 3-8 Equivalent Fractions and Mixed Numbers
Course 2
3-8
Equivalent Fractions and Mixed Numbers
In some recipes the amounts of ingredients are given as fractions, and sometimes those fractions do not equal the fractions on a measuring cup. Knowing how fractions relate to each other can be very helpful.
Different fractions can name the same number. 3 5 6 10 15 25 = =

5. 3-8 Equivalent Fractions and Mixed Numbers
Course 2
3-8
Equivalent Fractions and Mixed Numbers
In the diagram = These are called equivalent fractions because they are different expressions for the same nonzero number. 3 5 6 10 15 25 =
To create fractions equivalent to a given fraction, multiply or divide the numerator and denominator by the same number. 3 5
3 · 2
5 · 2 6 10 15 25
15 ÷ 5
25 ÷ 5 3 5 = = = =

6. 3-8 Equivalent Fractions and Mixed Numbers Remember! 3
Course 2
3-8
Equivalent Fractions and Mixed Numbers
Remember!
is in simplest form because the greatest
common factor of 3 and 5 is 1. 3 5

7. Additional Example 1: Finding Equivalent Fractions
Course 2
3-8
Equivalent Fractions and Mixed Numbers
Additional Example 1: Finding Equivalent Fractions
Find a fraction equivalent to the given fraction. 5 7 A. 5 7
5 · 3 15 21 =
Multiply numerator and
denominator by 3. =
7 · 3 18 24 B.
Divide numerator and
denominator by 2. 18 24
18 ÷ 2
24 ÷ 2 9 12 = =

8. Insert Lesson Title Here
Course 2
3-8
Equivalent Fractions and Mixed Numbers
Insert Lesson Title Here
Try This: Example 1
Find a fraction equivalent to the given fraction. 3 8 A. 3 8
3 · 2 6 16 =
Multiply numerator and
denominator by 2. =
8 · 2 6 12 B. 6 12
6 ÷ 3
12 ÷ 3
Divide numerator and
denominator by 3. 2 4 = =

9. 3-8 Equivalent Fractions and Mixed Numbers
Course 2
3-8
Equivalent Fractions and Mixed Numbers
To determine if two fractions are equivalent, find a common denominator and compare the numerators.
You can also put both fractions into simplest form and see if they are equal.

10. Additional Example 2A: Determining Whether Fractions are Equivalent
Course 2
3-8
Equivalent Fractions and Mixed Numbers
Additional Example 2A: Determining Whether Fractions are Equivalent
Write the fractions with a common denominator. Then determine if they are equivalent. 4 6 28 42
A and
Both fractions can be written with a denominator of 3. 4 6
4 ÷ 2
6 ÷ 2 2 3 = = 28 42
28 ÷ 14
42 ÷ 14 2 3 = =
The numerators are equal, so the fractions are
equivalent.

11. Additional Example 2B: Determining Whether Fractions are Equivalent
Course 2
3-8
Equivalent Fractions and Mixed Numbers
Additional Example 2B: Determining Whether Fractions are Equivalent
Write the fractions with a common denominator. Then determine if they are equivalent. 6 10 20 25
B and
Both fractions can be written with a denominator of 50. 6 10
6 · 5
10 · 5 30 50 = = 20 25
20 · 2
25 · 2 40 50 = =
The numerators are not equal, so the fractions are
not equivalent.

12. Insert Lesson Title Here
Course 2
3-8
Equivalent Fractions and Mixed Numbers
Insert Lesson Title Here
Try This: Example 2A
Write the fractions with a common denominator. Then determine if they are equivalent.
A and 3 9 6 18
Both fractions can be written with a denominator of 3. 3 9
3 ÷ 3
9 ÷ 3 1 3 = = 6 18
6 ÷ 6
18 ÷ 6 1 3 = =
The numerators are equal, so the fractions are
equivalent.

13. Insert Lesson Title Here
Course 2
3-8
Equivalent Fractions and Mixed Numbers
Insert Lesson Title Here
Try This: Example 2B
Write the fractions with a common denominator. Then determine if they are equivalent. 4 12 9 48
B and
Both fractions can be written with a denominator of 96. 4 12
4 · 8
12 · 8 32 96 = = 9 48
9 · 2
48 · 2 18 96 = =
The numerators are not equal, so the fractions are
not equivalent.

14. 3-8 Equivalent Fractions and Mixed Numbers 8 5 3 5 = 1 8 5 3 5
Course 2
3-8
Equivalent Fractions and Mixed Numbers 8 5 3 5
is an improper 1
is a mixed
fraction. Its
numerator is
greater than its
denominator.
number. It
contains both a
whole number
and a fraction. 8 5 3 5
= 1

15. 3-8 Equivalent Fractions and Mixed Numbers 
Course 2
3-8
Equivalent Fractions and Mixed Numbers
Additional Example 3: Converting Between Improper Fractions and Mixed Numbers 13 5
A. Write
as a mixed number.
First divide the numerator by the denominator. 13 5 3 5
Use the quotient and remainder to
write a mixed number.
= 2 2 3
B. Write 7
as an improper fraction.
First multiply the denominator and whole number,
and then add the numerator. +
Use the result to
write the improper
fraction. 2 3
3 · 7 + 2 23 3 = 7 = 3 

16. 3-8 Equivalent Fractions and Mixed Numbers  Try This: Example 3
Course 2
3-8
Equivalent Fractions and Mixed Numbers
Try This: Example 3 15 6
A. Write
as a mixed number.
First divide the numerator by the denominator. 15 6 3 6 1 2
= 2
Use the quotient and remainder to
write a mixed number.
= 2 1 3
B. Write 8
as an improper fraction.
First multiply the denominator and whole number,
and then add the numerator. +
Use the result to
write the improper
fraction. 1 3
3 · 8 + 1 25 3 = 8 = 3 